Sequence for learning progression in geometry:
(3 steps)
Front
1. The student sorts, identifies, describes by manipulating concrete models
2. The student classifies geometric shapes using their properties
3. The student makes/ test hypothesis using their properties
Back
Efficiency
Front
When students do not get caught up in too many steps
Back
Informal deduction (Abstract)
Front
Can recognizing relationships between & among properties of shapes or classes of shapes and follow logical arguments
Back
Cubes
Front
"Snapcubes"
Back
Subitize
Front
Instantly recognize without counting
Back
Chronometers
Front
Back
Pattern Blocks
Front
Back
Depth of Knowledge (4 Levels)
Front
Back
Simulations
Front
Where students interact in a reality/experimental learning
Monopoly is a simulations NOT considered a game
Back
Rate
Front
Tracking how many exercises were correctly done in a certain amount of time
Back
Naturalistic Assessment
Front
Based in natural setting of classroom (Observation)
Back
Analysis (Analytic)
Front
Able to identify properties of shapes and is learning to use appropriate vocabulary related to properties
Back
Assessment should be:
Front
Ongoing and summative (We should not teach then assess)
Back
Combination Problems
Front
Involve diff. combinations (2 pants & 2 shirts)
Back
1. Recalls Information
Front
Back
Algebra Tiles
Front
Back
Area & Array Problems
Front
Finding the rectangular area or arrangement
Back
NCTM
Front
National Council of Teachers of Mathematics
Back
Automaticity
Front
instant recall of a math fact without having to think about it
Back
Manipulatives
Front
Concrete level tools to help visualize math concepts
Back
Deduction
Front
Able to go beyond identifying characteristics of shapes using definitions, axioms
Back
Think Alouds
Front
Teacher says out loud what they are thinking when problem solving
Back
Natural Numbers
Front
Back
Accuracy
Front
Careful recording, checking correctness of the results
Back
a + (b + c) = (a + b) + c
a(bc) = (ab)c
Front
Associative Property
Back
Iteration
Front
Used to express the length of an object
Back
2. Basic Application of Concepts & Skills
Front
Back
C2
Front
Back
a + 0 = a or a x 1 = a
Front
Identity
Back
GCF
Front
The greatest factor that divides two numbers
Back
LCM
Front
The smallest number that they both divide evenly into
Back
Mult or Divi Problems:
Front
Back
4. Extended Thinking & Complex Reasoning
Front
Back
Composite Numbers
Front
Back
Visualization (Descriptive)
Front
Can name and recognize shapes by their appearance & characteristics
Back
ab=ba or a + b = b + a
Front
Communicative Property
Back
Equal Groups Problems or Repeated Addition
Front
3 groups of 6 or 3 x 6 or 6 + 6 + 6
Back
3. Strategic Thinking & Complex Reasoning
Front
Back
T or F:
Problem solving & application of math should come after mastery of skills
Front
FALSE
Back
Cuisenaire Rods
Front
Back
Alternate Assessment
Front
Portfolio's, Journals, Projects
Back
Base-ten Blocks
Front
Back
C1
Front
Back
Assessment in math should be
Front
Holistic (All diff. types)
Back
Flexibility
Front
Students are able to use more than one approach
Back
Objective Assessment
Front
T/F. Yes or No, Multiple Choice
Back
Prime Number
Front
Back
Color Tiles
Front
Back
Multiplicative Comparison Problems
Front
Involve finding "How many more times as much" or "stretching" the original quantity by a certain quantity
Back
Section 2
(47 cards)
Gold from Arizona and Colorado...
Front
260,000
Back
Polyhedron
Front
3-Dimensional figure
Faces: are polygons
Edges: outside perimeter
Vertex (Vertices): 2 or more straight lines meet
Back
Equilateral Triangle
Front
Triangle with ALL equal sides
Back
Compensation:
Front
Rounding with still finding the exact amount
Ex. 285 - 99
286 + 100
Back
Box has 1.5 lbs of nuts...8 oz
Front
3 boxes
Back
Polygon
Front
2-Dimensional figure
Back
Avg. adult male height?
Front
180 cm
Back
Avg. span kids arm is 100 cm, want to cover a track thats . km. How many kids do they need?
Front
500
Back
Perimeter:
Front
Distance around a polygon
Back
Polyherdron with 6 faces, 8 vertices, and 12 edges
Front
Cube
Back
b=a/c
Front
Provided c is not equal to zero
Back
Building a walkway around a pool. Can't exceed an area of 190. The pool measures 12 by 8, how much area?
Front
94
Back
Reflection:
Front
Flipped across a line, creating a mirror image
Back
Which number is the largest?
Front
2/.6
Back
Isosceles Triangle
Front
Triangle with 2 equal sides
Back
1. Front-end
Front
Involves adding the front digits together
345 + 675
3 + 6 = 9
900
Back
Numerator/Denominator
Front
3/4
3 is the numerator
4 is the denominator
Back
Turtle Population...
Front
By year 2050
Back
Dilation:
Front
Transformation that produces an image that is the same shape as the original, but is a different size
Back
Numeral:
Front
The symbolic form of a number
Back
4. Compatible (Friendly) Numbers
Front
Back
Non-polyherda:
Front
Cylinders, Cones & Spheres
Back
Irrational Numbers:
Front
infinite and non-repeating decimals
Back
What tool do you use for place value?
Front
Base ten blocks
Back
Area:
Front
Amount of surface that a shape covers
Back
Volume:
Front
Amount of space a shape contains
Back
5. Special Numbers
Front
Back
Est size of Rhode Island?
Front
3,140km
Back
Circumference:
Front
Distance around a circle
Back
Estimating Strategies (5 types)
Front
Back
Which shape cannot be a quadiliterial?
Front
Pentagon
Back
Development Progression:
Front
1. Reciter
2. Counter
3. Producer
Back
C5
Front
Back
C3
Front
Back
3. Clustering
Front
Works well then the numbers are close together
37 + 68 + 13
37 + 13 = 50 so 50 + 70 = 120
Back
Doubling
Front
Doubling and halving
Back
Scalene
Front
Triangle with NO equal sides
Back
2. Rounding
Front
Rounding the numbers to the nearest 10 or 100
345 + 675
300 + 700 = 1,000
Back
200 fish were caught and tagged...
Front
625
Back
Avg. Temp of human?
Front
37 degrees Celsius
Back
Best unit to weight a person?
Front
KG
Back
Someone works 40 hrs a week...How much will they make overtime?
Front
$962
Back
Athlete swam 100 yards in 52 seconds...
Front
5.8 ft per second
Back
Rotation:
Front
Figure turns around a fixed center point
Back
Real Numbers:
Front
the set of rational numbers a/b
Back
Translation:
Front
Same size. Every point of the object must be moved in the same direction and for the same distance.